The following relates to the information processing arts, computational arts, inference arts, and related arts.
Numerous applications entail inference based on integration over probabilistic information. For example, optimal control systems use integration over possible (i.e., probabilistic) responses of a controlled system to a control input in order to estimate system response to the control input. Bayesian inference systems integrate a hypothesis probability density function over accumulating evidence in order to refine the hypothesis. Bayesian inference is used for classification systems and diverse predictive systems and other systems that process uncertain information.
In the case of multidimensional data, such integrals often cannot be computed analytically. Moreover, conventional numerical integration techniques such as Riemann sums can be computationally impractical for high-dimensionality integrals used in control systems or other real-time or otherwise time-constrained systems employing inference engines.
Approximate integration solutions have been developed, such as the mean field approximation. In these approximate integration solutions, the function to be integrated is approximated by a more tractable function that can be analytically integrated. These approaches rely upon the more tractable function being a satisfactory approximation to the actual function to be integrated. In many applications, the function to be integrated may be multimodal or otherwise complex, with the detailed topology, number and position of modes, or other complexity of the function being unknown and not readily estimated. In such applications, the accuracy of the approximate integration is not known a priori, and may be poor (indeed, arbitrarily poor) in certain instances. Such integration solutions with variable and potentially poor accuracy are not well suited for use in task-critical applications such as optimal control or Bayesian inference.